Lord Thomas (right) is boycotting Mr Asghar's meeting with the ambassador
The assembly's presiding officer is calling on AMs to boycott a private meeting with the Israeli ambassador, organised by Wales' only Muslim AM.
Lord Dafydd Elis-Thomas said he objected to Israel's "failure to meet its international obligations" towards the Palestinians.
Mohammed Asghar, who represents South Wales East, invited his assembly colleagues to the confidential meeting.
But Lord Elis-Thomas e-mailed the AMs calling on them to refuse to attend.
The leaders of the political groupings in the assembly have been invited to meet Ron Prosor during a visit to the Senedd in Cardiff Bay this month in an event arranged by the assembly government.
Mr Asghar, the first AM from an ethnic minority, said his own invitation to Mr Prosor, which was sent internally and marked as confidential, aimed to promote inter-faith dialogue.
Speaking on BBC Radio Wales, Mr Asghar explained his decision.
He said: "The biggest flashpoint in the world at the moment is the Israeli-Palestinian conflict, so we must understand both sides of the facts.
The Israeli ambassador was invited by the assembly's only Muslim AM
"I know quite a lot from the Palestinian side, but I haven't been able to speak with any Israeli till today, so in my fortunate position I thought this was the best opportunity for me to invite him.
"That was the whole idea, to bring him over, and listen to his views.
"I don't want to put my head in the sand, and I appreciate everybody's feelings, and being Muslim, probably everyone knows my feelings, but I am a human being, and a peaceful human being.
"I'm sure everyone's got their own mind to make and I'm sure some of them, most of them, will love to listen to Ron Prosor and I will pledge again when I see Lord Elis-Thomas in the next couple of days to change his mind."
In his leaked e-mail, Lord Elis-Thomas said: "I am unwilling to accept the invitation to meet the ambassador because of my objection to the failure of the state of Israel to meet its international obligations to the Palestinian people of the Holy Lands. I would invite other colleagues to do the same."
Rodney Berman, the leader of Cardiff council, said Wales' Jewish community would be shocked at the "strident tone" of Lord Thomas's response.
He said: "If AMs have concerns, as I do myself, about policies followed by the Israeli government then surely it's better to use this event to talk about those concerns rather than to put up barriers which can only promote further misunderstanding."
Jean Evans, UK Co-ordinator of the Israel Peace Forum, based in Cardiff, called Lord Elis-Thomas's position "absolutely appalling", and said it would only stir up more trouble and drive people apart.
Lord Elis-Thomas was not commenting on his leaked e-mail but was said to be standing by what he had written.
A Welsh Assembly Government spokesman said: "This will be the new Ambassador's first visit to Wales at the request of the Israeli Embassy. He will be meeting the First Minister to familiarise himself with our country and what Wales has to offer the world."
The Israeli embassy has been asked to comment.
Meanwhile, the conduct of the presiding officer is to be included as a formal item on the agenda of the next meeting of the assembly's Labour group.
One senior Labour AM described his boycott as "discourteous" to Mr Asghar.
Rhondda AM Leighton Andrews told Mr Asghar that the presiding officer's e-mail was "insulting to the people of Israel, and demeaning to the national assembly."
Mr Andrews accused Lord Elis Thomas of "juvenile gesture politics".